Analysis of the Global Research Status of Graph Theory Based on

Bibliometrics

Furui Chen

1,* a

and Yubin Hu

School of Political Science and Public Administration, Soochow University, Suzhou, Jiangsu, China

College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou, Jiangsu, China

Keywords: Graph Theory, Bibliometrics, Development Trend, Visual Analysis.

Abstract: Graph theory, as a branch of operations research, has an ancient research history. In recent years, it has not

only broken new ground in its applications but also optimized its existing models with the help of new tools

such as neural networks and machine learning. Based on the Web of Sciences core database, this paper

analyses the number of annual papers, core authors, disciplinary layout, countries, and keywords. Using the

visual analysis software CiteSpace and VOSviewer, we can comprehensively reveal research trends, research

capabilities, and research directions Hotspots in the field of graph theory from 2012 to 2021. The results show

an overall upward trend in the development of graph theory research, with two countries, led by China and

the United States, dominating most of the research worldwide and collaborating to some extent. The research

direction of graph theory has also evolved from expanding applications to optimization models.

1 INTRODUCTION

Many real-world situations can conveniently be

described using a diagram consisting of a set of points

together with lines joining specific pairs of these

points. Notice that in such diagrams, one is mainly

interested in whether or not a line joins two given

points; how they are joined is immaterial. A

mathematical abstraction of situations of this type

gives rise to the concept of a graph (Bondy 1976). The

graph theory problem can be traced back to Euler's

1736 paper on the Seven Bridges Problem. As an

independent branch of mathematics, it is

characterized by simple models and strong

generalization. It is good at describing the

relationship between two things, so it has been widely

used in various fields such as management science,

computer science, and biology and has achieved

fruitful results. With society's development, new

methods such as deep learning and neural networks

are emerging to innovate and optimize theoretical

graph models.

On the other hand, theoretical graph models are

being applied to more research areas. With the

continuous development of modelling and solving

https://orcid.org/0000-0002-2689-7747

https://orcid.org/0000-0001-6350-8096

graph theoretical problems, there is an urgent need for

systematic analysis and review of the existing

research. Therefore, in this paper, we use a

bibliometric approach to organize and summarize the

research literature in this field in the past ten years

from different perspectives, summarize the relevant

publications, and show the development paths,

research hotspots, and possible future trends of graph

theory through data visualization.

2 MATERIALS AND METHODS

To ensure the authority and coverage of the analysed

data, the data source was selected as Web of Science

(Core Collection), the index was selected as SCI-

Expended and SSCI, and the search strategy was

selected as (TS= ("graph theory")), the period was

January 2012 to December 2021, the search

document type was Articles, and the language was

English. After screening and de-weighting, a total of

10124 papers were obtained. Please remember that all

the papers must be in English without orthographic

errors.

Chen, F. and Hu, Y.

Analysis of the Global Research Status of Graph Theory Based on Bibliometrics.

DOI: 10.5220/0012071300003624

In Proceedings of the 2nd International Conference on Public Management and Big Data Analysis (PMBDA 2022), pages 147-153

ISBN: 978-989-758-658-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

147

Bibliometrics refers to the application of

mathematics and statistical methods to books and

other forms of written communication (Pritchard

1969). It is a quantitative research method based on

publications, citations, and textual data to describe

and analyse the dynamics and progress of a discipline

or research field (Van 2019). A bibliometric study's

results include descriptive statistics and an analysis of

keywords, texts, citations, authors, and their

associated networks. It examines the frequency,

relevance, centrality, and clustering of the author and

textual data. Therefore, scholars often use it to

explore the evolutionary patterns, publication trends,

author citation networks, and other elements of a

topic. In this paper, we use two visualization tools

called VOSviewer and CiteSpace to conduct a

bibliometric study.

3 DESCRIPTIVE STATISTICS

3.1 Basic Quantitative Information

The 10124 papers used in this study were written by

29669 authors from 6004 organizations in 115

countries, published in 2063 journals, and cited

246046 references from 49818 journals.

3.2 Analysis of Papers’ Annual

Amount

The number of published papers in a research field

can reflect the research results of the field in a specific

period. It can be used as an indicator to measure the

development trend of a field, visually demonstrating

the level of development, the speed of development,

and the research activity in that field. Figure 1 shows

the annual publication volume and growth rate of

graph theory thematic literature from 2012 to 2021.

In the past ten years, the overall publication trend of

graph theory-related literature has been steadily

increasing, especially in the past five years. The

annual growth rate of the number of publications is

not less than 10%, which reflects the tenacity of graph

theory and the attention of more and more scholars.

Figure 1: Number and growth rate of papers published from 2012 to 2021.

3.3 Analysis of Journals

The table below shows the top 10 journals regarding

the number of articles published, citations, and

average citations per page. From this, we can see that

the topics of most journals are related to biology and

the nervous system. In addition, the top four journals

in terms of citations per article are all related to

neurology, reflecting that papers on related topics are

more likely to be used by other scholars. Meanwhile,

only a few journals are general or related to discrete

mathematics and other directions.

Table 1: Top 10 Journals.

SN Source Quantity

Average

Citation

JOURNAL OF

GRAPH THEORY

203 5.51

2 IEEE ACCESS 184 7.28

3 NEUROIMAGE 167 48.55

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HUMAN BRAIN

MAPPING

135 27.15

5 PLOS ONE 125 45.01

SCIENTIFIC

REPORTS

106 14.78

NEUROCOMPUTI

100 20.15

DISCRETE

APPLIED

MATHEMATICS

99 4.13

FRONTIERS IN

HUMAN

NEUROSCIENCE

80 27.95

IET CONTROL

THEORY AND

APPLICATIONS

80 17.56

3.4 Analysis of Discipline Layout

Based on the classification of Web of Science, a

scientific layout analysis of papers on the research

topic of "Graph Theory." Table 2 shows the situation

of the top 10 disciplines in the classification of global

papers in the field of graph theory from 2012 to 2021

in all 200 disciplines. This includes Engineering

Electrical Electronics in first place with 16.58% and

Neuroimaging in tenth place with 5.03%, which

shows that the research application of graph theory

has a more balanced distribution and covers a large

area.

Table 2: Top 10 Categories.

SN Categories Quantity Proportion

Engineering

Electrical Electronic

1679 16.58%

2 Neurosciences 1582 15.63%

3 Mathematics 1306 12.90%

4 Mathematics Applied 1137 11.23%

Automation Control

Systems

800 7.90%

Computer Science

Information Systems

786 7.76%

Computer Science

Artificial Intelligence

649 6.41%

8 Telecommunications 592 5.85%

Multidisciplinary

Sciences

533 5.26%

10 Neuroimaging 509 5.03%

4 VISUAL ANALYSIS AND

DISCUSSION

4.1 Core Authors Analysis

Price pointed out that half of the articles on the same

topic are written by a group of highly productive

authors (Price 1963). Based on this theory, we

selected the authors with more than or equal to 5

publications as the core group of authors in this field

after trial calculation to understand the cooperative

relationship between core authors and provide a

reference basis for academic exchange, international

cooperation, and talent introduction (White 2003).

Figure 2 shows the network diagram with authors

as nodes; the more significant the node, the more

frequently the author appears in the research area.

Among them, Wenxue Li (80) started the research on

Coupled nonlinear systems based on graph theory in

2012 (Li 2012), became the core author with the most

posts, and has made several collaborations with

YanLiu and others. Qiyong Gong (47) started a

graph-theoretic analysis of topological connectivity

in the cerebral cortex in 2015 (Lei 2015). Siddiqui

and Muhammad Kamran (41) started to analyse the

topology of crystalline molecules as well as microbial

domains using graph theoretic methods in 2017,

obtaining more remarkable results in a short period

while collaborating more closely with Sharma

(Siddiqui 2017). We can see that the top three core

authors have conducted pioneering research using

graph theory methods in different fields at different

periods. This further reflects the enormous scope of

the application of graph theory methods.

In addition to the three authors mentioned above,

Table 3 shows the information of the top five core

authors in terms of the number of publications, from

which we can see that there are many high-quality

authors with 76.37 citations per article among the

authors with high number of publications.

Figure 2: Author Cooperation Network Map.

Analysis of the Global Research Status of Graph Theory Based on Bibliometrics

149

Table 3: Top 5 Core Author.

SN Author Quantity

Average

Citation

1 Li, Wenxue 80 14.2

2 Gong, Qiyong 47 23.76

3 He, Yong 43 76.37

Siddiqui, Muhammad

Kamran

41 12.39

5 Sharma, V. K. 36 6.35

Table 4: Top 10 Countries.

SN Country Quantity Citations Total link strength Average Citation Centrality

1 China 2962 52422 3422734 17.6981 0.10

2 USA 2370 56632 3623603 23.8953 0.26

3 England 647 14602 1367165 22.5687 0.18

4 Canada 521 12582 972406 24.1497 0.12

5 Germany 512 11233 950310 21.9394 0.11

6 France 477 7074 524488 14.8301 0.11

7 India 444 4763 266075 10.7274 0.06

8 Italy 381 7511 855841 19.7139 0.05

9 Spain 379 6105 601484 16.1081 0.13

10 Australia 354 10918 660672 30.8418 0.05

4.2 National Layout Analysis

The top ten countries with the number of publications

are listed in the table above.

It can be seen that among all countries, China and

the United States have significantly higher

publication numbers than other countries, accounting

for 29.25% and 23.40% of the total publications,

respectively, which reflects that China and the United

States are the leading force in graph theory research.

In terms of centrality, the U.S. is far ahead, followed

by the U.K. and Spain, which indicates that the three

have significant influence and play a central role in

the national cooperation network. Conversely, China

is ranked seventh, reflecting that there is still room for

improvement in its posting influence, which needs to

be improved further to deepen cooperation.

Using VOSviewer to visualize the state of country

cooperation, we find that the papers from both China

and the U.S. have an extensive impact range,

basically covering all the countries involved, which

shows that scholars worldwide in the field of graph

theory are expanding their research around these two

core countries.

Figure 3: Country Cooperation Network Map.

4.3 Research Institutions Analysis

The table below shows the number of articles

published by research institutions, from which we

find that 8 of the top 10 search institutions are from

China, which again reflects the quantitative

leadership of Chinese research. The highest average

citation among them is Beijing Normal University

(61.50), and the lowest is Harbin Institute Technology

at Weihai (14.01), with overall highs and lows and no

country-level differences.

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Table 5: Top 10 Institutions.

Institutions

Quantity

Average

Citation

Chinese Academy

of Sciences

159 31.67

Southeast

Universit

115 31.65

Harbin Institute of

Technology

115 17.18

Beijing Normal

University

114 61.50

Harbin Institute of

Technology at

Weihai

96 14.01

University of

Cambridge

92 44.12

University of

Electronic Science

and Technology of

China

88 25.44

University of

Illinois

84 16.46

9 Peking University 80 35.01

Huazhong

University of

Science and

Technolo

79 23.10

4.4 Keywords Co-Occurrence Analysis

Keywords summarize an article's gist and essence,

and keyword co-occurrence analysis can reveal

research priorities in a scholarly field (Wang 2022).

Therefore, we used CiteSpace to summarize the

keywords of 10124 documents and selected keywords

with occurrences greater than 30 for co-occurrence

analysis to obtain the following figure.

Figure 4: Keywords Clustering Map.

From this, we can see that keywords such as

functional connectivity, network, and organization

have become the core of the study of graph theory

problems. Then we can judge that most of the

research on graph theory in the last decade has been

conducted around the connectivity of systems. At the

same time, we found that the research on graph theory

is relatively close to each other in terms of keywords,

without any apparent split. To get a clearer picture of

the specifics of the keywords, the following table

shows the top ten keywords in terms of frequency of

occurrence.

Table 6: Top 5 Keyword.

SN Keyword Occurrences

Total link

strength

1 network 820 1533

2 connectivity 633 1461

3 model 556 827

functional

connectivity

508 1243

5 system 494 712

4.5 Keyword Emergence Analysis

Keyword emergence analysis refers to the analysis of

words that appear with high or high frequency in the

published literature of a research area over a specified

period. It is often used to determine the research

frontier or to predict the development trend (Yan

2022).

In this work, 25 emergent words with high

emergent values are determined using the software

CiteSpace. In connection with the further analysis of

the emergence intensity and duration, the limit

problems and the development trend of graph theory

research were investigated in this work. According to

the table below, we find that graph theory research in

the past decade is divided into two phases, the first

being the short two years from 2012 to 2013, in which

more than half of the emergent keywords appeared,

reflecting the expansion of graph theory research in

the application. The second phase is from 2014 to

2021, during which the number of emergent

keywords is smaller, but they are often related to

algorithmic theory, which reflects the progress of

graph theory research in algorithmic optimization of

the underlying model in recent years.

Table 7: Distribution of Research Hotspots in Each Stage.

Keywords Year 2012 - 2021

agent 2012

▃▃▃▂▂▂▂▂▂

▂

anatomical

network

2012

▃▃▃▃▃▂▂▂▂

▂

Analysis of the Global Research Status of Graph Theory Based on Bibliometrics

151

modular

organization

2012

▃▃▃▃▂▂▂▂▂

▂

cooperation 2012

▃▃▃▃▂▂▂▂▂

▂

small world 2012

▃▃▃▂▂▂▂▂▂

▂

including

solution

2013

▂▃▃▂▂▂▂▂▂

▂

cortical

network

2012

▂▃▃▃▂▂▂▂▂

▂

small world

network

2012

▂▃▃▃▃▂▂▂▂

▂

thermodynamic

property

2013

▂▃▃▂▂▂▂▂▂

▂

algebraic graph

theory

2013

▂▃▃▃▃▃▂▂▂

▂

graph

theoretical

anal

sis

2012

▂▃▃▃▃▂▂▂▂

▂

cycle 2013

▂▃▃▂▂▂▂▂▂

▂

habitat

fragmentation

2013

▂▃▃▃▃▃▂▂▂

▂

flocking 2013

▂▃▃▃▃▂▂▂▂

▂

global stability 2013

▂▂▃▃▃▃▂▂▂

▂

motion 2014

▂▂▃▃▃▂▂▂▂

▂

nonlinear

dynamics

2015

▂▂▂▃▃▃▂▂▂

▂

network theory 2017

▂▂▂▂▂▃▃▂▂

▂

drug naive 2017

▂▂▂▂▂▃▃▂▂

▂

time varying

delay

2017

▂▂▂▂▂▃▃▂▂

▂

reveal 2017

▂▂▂▂▂▃▃▂▂

▂

robustness 2015

▂▂▂▂▂▂▃▃▂

▂

clustering

algorithm

2019

▂▂▂▂▂▂▂▃▃

▃

stability

analysis

2018

▂▂▂▂▂▂▂▃▃

▃

stress 2019

▂▂▂▂▂▂▂▃▃

▃

5 CONCLUSIONS

As a classical class of operations research problems,

graph theory problems still have sufficient research

value and application prospects today. In this paper,

we use bibliometric methods and visualization

software such as CiteSpace and VOSviewer to

conduct descriptive statistics on the number of

publications, author information, and publication

institutions of graph theory-related literature in the

past ten years and conduct keyword emergence

analysis to explore the development trend of graph

theory problems in recent years.

To summarize, graph theory problems have

remained high in popularity in the last decade, used

in many fields, such as medicine and chemistry. In the

last five years, there has been a wave of underlying

optimization designs of algorithmic models. In this

process, we find that China, as the main force of

research, has a clear lead in both the number of

publications and the number of publishing institutions

but suffers from two problems: low author centrality

and obvious geographical limitations of institutional

cooperation, which make it difficult for Chinese

scholars' research to have a broader impact often.

Therefore, we suggest that China should strengthen

the level of cooperation between domestic and

foreign research, pay attention to the process of

training related talents, and broaden the field of graph

theory research applications as much as possible to

integrate industry, academia, and research better, and

let the benefits of scientific research shade the world.

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